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Sibirskii Matematicheskii Zhurnal, 2001, Volume 42, Number 3, Pages 670–682
(Mi smj1451)
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This article is cited in 14 scientific papers (total in 14 papers)
Energy error estimates for the projection-difference method with the Crank–Nicolson scheme for parabolic equations
V. V. Smagin Voronezh State University
Abstract:
We solve an abstract parabolic problem in a separable Hilbert space, using the projection-difference method. The spatial discretization is carried out by the Galerkin method and the time discretization, by the Crank–Nicolson scheme. On assuming weak solvability of the exact problem, we establish effective energy estimates for the error of approximate solutions. These estimates enable us to obtain the rate of convergence of approximate solutions to the exact solution in time up to the second order. Moreover, these estimates involve the approximation properties of the projection subspaces, which is illustrated by subspaces of the finite element type.
Received: 01.09.1998
Citation:
V. V. Smagin, “Energy error estimates for the projection-difference method with the Crank–Nicolson scheme for parabolic equations”, Sibirsk. Mat. Zh., 42:3 (2001), 670–682; Siberian Math. J., 42:3 (2001), 568–578
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